Weak-electromagnetic unification and broken S4 symmetry

A left-right symmetrical model on weak-electromagnetic unification with four neutral gauge particles obeying S₄ symmetry in their mass generation mechanism is proposed. The Weinberg-Salam results are obtained with sin²θ_w fixed naturally to be 0.25, and further results about superweak interactions are also given.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Radiative quark masses constrained by the gauge group only

We discuss the possibility of obtaining the observed pattern of quark masses and mixings as a consequence of radiative corrections, gauge invariance and particle content of the theory. We do not allow any kind of additional symmetry, such as family and discrete symmetries. A model based on the gauge groupSU(3)×SU(2) _L ×SU(2) _R ×U(1) _B?L is considered. It turns out that the correct values of quark masses can be reasonably reproduced. The typical strength of the flavour changing couplings of theZ ⁰-boson is however at least one order of magnitude above the experimental upper bounds. A comparison is made with a model in which an additional discrete symmetry is present. In this case flavour changing phenomena can be kept under control.     

Weak correction to the muon magnetic moment in a gauge model

The weak correction, a_μ^w, to the anomalous magnetic moment of the muon is calculated in an SU(2) ? U(1) ? U(1) gauge model of weak and electromagnetic interactions. The R_ξ gauge is used and Ward-Takahashi indentities are utilized eliminating all ξ-dependence before the loop integration is performed. a_μ^w,expt places no constraint on the mass of one of the neutral vector mesons, which may be arbitrarily small.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Gauge symmetry breaking in compact multiply connected manifolds

In a multiply connected manifold, M₄⊗S₃/Z², we compute at one-loop level the gauge symmetry breaking due to Wilson loops. For an SU(3) model without matter fields a non-trivial vacuum, which breaks the gauge symmetry has lower energy.     

Chiral U(1) symmetry and weak neutral currents at high energy

If chiral U(1) symmetry is a gauge symmetry, CP is automatically conserved despite the instanton effects, and the weak neutral currents have a definite structure. A realistic SU(2) _L ?U(1)?U(1) _R model contains an axion which is consistent with present data. Furthermore the neutrino interactions to lowest order are identical to the Weinberg-Salam model. Implications for the chiral U(1) currents are discussed.     

On the relation between the normal fluid density and the one particle Green function for Bose fluids

The normal fluid density is defined through the moment of inertia of a cylinder rotating about its axis, in the limit of infinitesimal angular velocity. The angular momentum may be calculated from the one particle Green function, and this leads to the relation between ?_n and the Green function.We then consider an ensemble in which the fluid is constrained to irrotational flow. For statistical states which are “locally gauge invariant” we show that ρ_n, as defined previously, is identical to the full density. This demonstrates the connection between superfluidity and the breaking of local gauge symmetry.Finally, we apply the result to the gas of non-interacting quasi-particles and the fully interacting Bose fluid in the limit of very low temperatures. In both cases we reproduce the Landau expression for ρ_n in terms of the quasiparticle occupation numbers, and derive the well-known result for real superfluid helium that ρ_n ～ T⁴ as T→0.     

Comments on intermediate-scale models

Some superstring-inspired models employ intermediate scales m₁ of gauge symmetry breaking. Such scales should exceed 10¹⁶ GeV in order to avoid prima facie problems with baryon decay through heavy particles and non-perturbative behaviour of the gauge couplings above m_I. However, the intermediate-scale phase transition does not occur until the temperature of the Universe falls below O(m_w), after which an enormous excess of entropy is generated. Moreover, gauge symmetry breaking by renormalization group-improved radiative corrections is inapplicable because the symmetry-breaking field has no renormalizable interactions at scales below m_I. We also comment on the danger of baryon and lepton number violation in the effective low-energy theory.     

The Dirac Equation in Six-dimensional <Emphasis Type="Italic">SO</Emphasis>(3,3) Symmetry Group and a Non-chiral “Electroweak” Theory

We propose a model of electroweak interactions without chirality in a six-dimensional spacetime with 3 time-like and 3 space-like coordinates, which allows a geometrical meaning for gauge symmetries. The spacetime interval ds ²=dx _μ dx ^μ is left invariant under the symmetry group SO(3,3). We obtain the six-dimensional version of the Dirac gamma matrices, Γ _μ , and write down a Dirac-like Lagrangian density, \(\mathcal{L}=i\bar{\psi}\Gamma ^{\mu }\nabla _{\mu }\psi\). The spinor ψ can be decomposed into two Dirac spinors, ψ ₁ and ψ ₂, interpreted as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields appear as parts of the same entity in a natural manner. The SO(3,3) Lorentz symmetry group is locally broken to the observable SO(1,3) Lorentz group, with only one observable time component, t _z . The t _z -axis may not be the same at all points of the spacetime, and the effect of breaking the SO(3,3) spacetime symmetry group locally to an SO(1,3) Lorentz group, is perceived by the observers as the existence of the gauge fields. We interpret the origin of mass and gauge interactions as a consequence of extra time dimensions, without the need of introducing the so-called Higgs mechanism for the generation of mass. Further, in our ‘toy’ model, we are able to give a geometric meaning to the electromagnetic and non-Abelian gauge symmetries.     

Models for the weak parity-violating vector meson exchange potential and the circular polarization in n + p → d + γ

We propose three models which lead to a p.v. nucleon-nucleon interaction mediated by charged and neutral vector mesons. Besides the ad hoc hypothesis of octet dominance, we consider two quark models (the Bose quark and colour Fermi quark model), which give a dynamical explanation of the $\text{ΔI =}\text{1}\text{2}$ rule in strangeness changing hyperon decays. They lead to p.v. potentials with different isospin dependence. We also derive the weak NN?_ρ° coupling from a SU(2) × U(1) gauge theory with neutral currents. The circular polarization P_γ of the γ-quanta in the capture of thermal neutrons on protons is calculated for these different models. The Reid hard-core (HC) and soft-core (SC) potentials have been chosen to take into account the strong interaction. Then the naively factorized Cabbibo current-current interaction with charged rho exchange only gives P_γ^HC = ?2.7 × 10^?8 and P_γ^SC = ?2.1 × 10^?8. The strong octet dominance and Bose quark model lead to a vanishing circular polarization |P_γ| ≈ (1–4) × 10^?9. The colour Fermi quark model enhances the circular polarization and gives P_γ ≈ ?5 × 10^?8.     

Electron paramagnetic resonance and electron nuclear double resonance of NaCl:Rh2+: A comparison between similarly doped Bridgman- and solution-grown single crystals

In a recent electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) study several new rhodium related centres in a Bridgman-grown crystal were reported. For two centres a detailed microscopic model was established. The primary Rh²⁺ centre was identified as a [RhCl₆]^4? complex with a single charge compensating Na⁺ vacancy in a next nearest neighbour position. A second centre was identified as a rhodium dimer. Two other Rh²⁺ centres, with apparent axial symmetry, remained unidentified. In the present study a detailed comparison between Rh²⁺ defects in Bridgman- and solution-grown NaCl crystals is presented. One of the previously unidentified Rh²⁺ centres is shown not to be axial but to have orthorhombic-I symmetry and is identified as a cis-[RhCl₆]^4? complex with two next nearest neighbour Na⁺ vacancies. For the primary centre additional ENDOR interactions confirm the model mentioned above. Finally a comparison is made between the temperature stability of the primary and orthorhombic-I centre in Bridgman-grown and similarly doped solution-grown NaCl crystals.     

Natural suppression of strong P and T non-invariance

In gauge theories with spontaneously broken left-right symmetry, strong P and T non-invariant effects can also be made to vanish naturally in the tree approximation without introducing massless quarks or axions. In a four-flavor SU(2)_L × SU(2)_R × U(1)_L+R model with manifest left-right symmetry, we show that strong CP noninvariance is absent up to the one-loop level and weak CP-violation is of superweak type. Extension to the case of six quarks gives a left-right symmetric generalization of the Kobayashi-Maskawa model without axions.     

Vibrational and electronic spectra of alkali halides doped with CrO42− ions

The i.r. spectra of alkali halides doped with FrO₄^2? ions are very sensitive to the concentration of background divalent impurities. Highly pure crystals containing CrO₄^2? ions show a 5 line i.r. spectrum in the v₃ stretch frequency region. One of these lines is attributed to CrO₄^2? ions in perfect crystal surroundings having T_d symmetry and the other 4 lines are attributed to C_s symmetry produced by a charge compensating anion vacancy in the nearest neighbour position. If the crystal contains a concentration of divalent cation impurity which is equal to or more than that of CrO₄^2? ions, a different spectrum characteristic of C_2x symmetry as well as the line corresponding to T_d symmetry are obtained. The crystals of ordinary purity contain all the three (C_s, C_2x and T_d symmetry) species and show eight line spectra. The changes in force constants calculated from the observed splitting of the energy levels agree with those evaluated from the known polarizability of the chromate ions.At 600°C, the vibration spectra of the highly pure crystals doped with CrO₄^2? ions show an increase in intensity of the line characteristic of T_d symmetry and the other lines practically disappear, because the anion vacancies move away from the neighbourhood of the CrO₄^2? ions at high temperatures. The energy of association of the vacancy with CrO₄^2? ions and the energy of migration of the vacancy are derived from the spectra obtained at different temperatures and with different heat treatments.The electronic spectra of the crystals show 3 bands (at 345, 270 and 240 nm for KCI). The lowest energy band has a fine structure with a spacing of about 800 cm^?1 at LAT. Since the transition involved is from a non-bonding to an antibonding state, the Condon parabola is shifted in the excited state and therefore the fine structure is attributed to a vibrational progression involving a totally symmetric frequency 800 cm^?1 in the excited state.     

A see-saw model of sterile neutrino

If the smallness of the mass of the sterile neutrino is to be explained by the see-saw mechanism, the off-diagonal entries of the mass matrix needs to be protected by some symmetry not far above the electroweak scale. We implement see-saw mechanism in a gauge model based on SU(2)^q_L×SU(2)^l_L×U(1)^q_Y×U(1)^l_Y un-unified gauge group which breaks to SU(2)_L×U(1)_Y at the TeV region via a two-step symmetry breaking chain. The right handed diagonal block is tied to the highest scale up to which the un-unification symmetry holds. The sterile neutrino emerges from a quark-lepton mixed representation of the un-unified group.     

Electronic and vibrational spectra of MnO2−4 in KBr crystals

Two new features have been observed in the electronic spectrum of KBr crystals doped heavily with MnO^2?₄ ions. The band at 870 nm is assigned to the crystal field transition e → t₂. The band at 600 nm shows a series of vibrational sub-bands at an interval of 740cm^?1 and is ascribed to the coupling between electronic transition and totally symmetric mode of the ion.A line at 830cm^?1, ascribed to totally symmetric mode v₁(A₁), has been observed for the first time in the Raman spectrum. I.R. spectrum of KBr: MnO^2?₄ shows four lines—one due to MnO^2?₄ in Td symmetry and the other three to the split components of v₃(T₂) for MnO^2?₄ in Cs symmetry. I.R. spectrum of KBr: MnO^2?₄: Ca²⁺ shows another s of four lines—one due to MnO^2?₄ in Td symmetry and the other three to the v₃(T₂) mode of the ion in C_2v symmetry. The v₁(A₁) line could not be observed in the i.r. spectra.     

A numerical estimate of the upper limit for the Higgs boson mass

TheSU (2) Higgs model with a scalar doublet field is studied by Monte Carlo calculations on 12⁴ and 16⁴ lattices. The gauge coupling is chosen to be similar in magnitude to the physical value in the standard model. The numerical results at large scalar self-coupling imply an upper limitm _H /m _W ?9 for the ratio of the Higgs boson mass to the W-mass.     

A new probe for local structure: Paramagnetic hyperfine structure in Nd3+ Mössbauer spectra

The⁴I_9/2 ground state of Nd³⁺ (4f³) is split by a crystal field of lower than cubic symmetry into five Kramer doublets. The magnetic hyperfine interactions can be calculated by using an effective magnetic hyperfine tensor Ã, which is obtained from the linear combination coefficients of the ground state doublet eigenvector. The hyperfine tensor à and the line shape depend strongly on the local structure of the system. Nondiagonal magnetic hyperfine interactions produce nonadiabatic relaxation. Corresponding lineshapes are calculated by means of the Clauser-Blume model and the eigenvalue treatment of superoperators. We found for Nd³⁺ in the investigated laser phosphate glass a network-forming function consistent with aC _3h orD _3h point symmetry.     

A theorem on electromagnetic properties of leptons

The following theorem is proven: Every lepton with the mass m, electric charge q and spin J belonging to any representation of a non-abelian gauge group must have the magnetic moment μ = qJm^?1, electric mean squared radius r² = qJ(J + 1)m^?2 and electric quadrupole moment Q = qJ(2J ? 1)m^?2 in the first order of the electromagnetic effects in an arbitrary renormalizable theory with the non-abelian gauge group symmetry which permits the validity of the Gerasimow-Drell-Hearn and Cabibbo-Radicati sum rules. The formula for the magnetic moment applies also for an abelian symmetry and remains valid even if the gauge symmetry is spontaneously broken.